Does anyone have suggestions for potential control variates for vanillas in a Heston model? I've tried black scholes with implied volatility, average volatility and long term volatility all without great success, so I'm hoping you guys got an idea.
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$\begingroup$ Are your vanillas American or European exercise? What pricing algorithm are you using? $\endgroup$– Brian BSep 30, 2013 at 13:58
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$\begingroup$ European. I've implemented Kaya-Broadie, full trunctuation and naive euler, but I'm willing to change if that makes it easier :) $\endgroup$– htdSep 30, 2013 at 17:23
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Glassermans's book suggests the stock price as the default idea for a control variate. In this paper, "Efficient, almost exact simulation of the Heston stochastic volatility model", by Haastrecht and Pelsser, (2008) the authors claim that this approach also works well for the Heston model (see appendix A2).
The book is very approachable and available online: Monte Carlo Methods in Financial Engineering, Paul Glasserman, 2003.